Suter was booed when he had the puck, and Parise was jeered after he scored his first goal. Both players have become unpopular in the Motor City because they turned down deals from Detroit to sign with Minnesota last summer.
"Of course, you heard them," Zetterberg said.
Detroit's new captain also heard a lot of sighs and groans early in the game from red-and-white clad fans when the Wild dominated play for much of the scoreless first period.
"They gave us what we deserved because we weren't playing well," Zetterberg said. "Fans are very engaged here; that's why this is a great place to play."
Detroit wanted to keep its depleted roster stacked with talent last July by making offers to Suter and Parise, the top two free agents, but both chose to play together in Minnesota with matching 13-year, $98-million contracts.
Parise, though, said the Red Wings were definitely one of the teams he was very interested in playing for this season.
"They're just a great organization. I have a lot of respect for them," Parise said. "They do things the right way. They play the game the right way. That was a tough one, because it's a really good place to play."
Pavel Datsyuk, who assisted on Zetterberg's goal, put Detroit ahead by two late in the second period. Datsyuk also set up Bertuzzi on his second goal that gave the Red Wings a 5-2 lead.
Parise's second goal of the game banked in off Zetterberg to pull the Wild within two midway through the third period.
Jimmy Howard made 23 saves for the Red Wings, who were outshot 11-6 in the first.
"Howard was good early when we struggled with the puck," Detroit coach Mike Babcock said
Minnesota's Josh Harding gave up four goals on 17 shots in the first two periods and finished with 22 saves.
"You're looking at the goals, which one could you fault him on?" Wild coach Mike Yeo asked. "There are times the puck goes in the net and there's nothing you can do."
The Red Wings scored two power-play goals in the second period after failing the first 17 times they had an advantage over their first three-plus games this season. Detroit's special teams breakthrough leaves the defending Stanley Cup champion Los Angeles Kings as the NHL's only team without a goal on the power play in the lockout-delayed season that started last weekend.
Red Wings rookie Damien Brunner took advantage of extra space on a power play, racing up the right side of the ice to score off an assist from Zetterberg, his Swiss league teammate during the lockout, for the game's first goal 13 seconds into the second period.
"That's why they signed him, to shoot the puck like that," Bertuzzi said.
Bertuzzi redirected the puck past Harding 42 seconds later to give Detroit a 2-0 lead. He made his season debut after missing the first three games because of the flu. Bertuzzi was originally diagnosed with mononucleosis, an ailment he said would have prevented him from playing for at least a month.
The rugged forward, who will turn 38 next week, made the most of his opportunity to play with Datsyuk. Babcock separated him from Zetterberg for the first time this season.
"I'm very lucky at this age to be playing with a world-class player like that," Bertuzzi said.
Detroit's second-period cushion didn't last long.
Parise scored off an assist from Suter, who got his first point with the Wild, at 2:49 of the second during a 5-on-3 power play. Tom Gilbert made it 2-all 6:29 into the period.
Zetterberg's first goal of the season gave the Red Wings the lead back, and Datsyuk restored their two-goal advantage.
The two stars will have to carry a rebuilding team this season that is trying to compete without seven-time Norris Trophy winner Nicklas Lidstrom and net-front specialist Tomas Holmstrom, both of whom retired. Voids were also created when defenseman Brad Stuart was traded to San Jose, a team he would have likely signed with if he wasn't dealt. Forward Jiri Hudler left to sign with Calgary.
"That's still an elite team, especially when you give them space with the puck," Harding said. "They've got a lot of guys who can score when they get a chance."